Q9 / 82 · NTA Abhyas (JEE Main) 2020 · Mathematics · Quadratic Equation

If $α$ is a root of the equation $4 x^{2} + 2 x - 1 = 0$ and $f (x) = 4 x^{3} - 3 x + 1,$ then $2 (f (α) + (α))$ is equal to

A
$- 1$
B
$0$
Correct answer
C
$1$
D
$2$

Solution

4 α^{2} + 2 α - 1 = 0

2 (f (α) + (α)) = 2 (4 α^{3} - 3 α + 1 + α)

= 2 (α (4 α^{2}) + (1 - 2 α))

= 2 (α (1 - 2 α) + (1 - 2 α))

= 2 (α - 2 α^{2} + 1 - 2 α)

= 2 (- 2 α^{2} - α + 1)

= - 4 α^{2} - 2 α + 2

= - 1 + 2 = 1

Hence, the correct answer is option: 'C'.

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